A degeneracy-weighted shell distribution governed by a single effective parameter, β, quantifies concentration toward near-optimal independent sets. Junwoo Jung and Jaewook Ahn at the KAIST, extracted the genuine concentration effect in quantum data by applying identical postprocessing to both experimental bitstrings and randomly generated bitstrings with matched excitation density, constructing an excitation-matched random baseline. Experiments on programmable Rydberg-atom arrays with system sizes up to 125 sites show quantum annealing consistently exceeds the random baseline, demonstrating enhanced concentration toward low-energy solution structure beyond what can be attributed solely to excitation density. Quantum annealing achieves exponential gains in solution sampling efficiency for combinatorial optimisation Quantum annealing represents a promising paradigm for tackling complex combinatorial optimisation problems, offering the potential to surpass the limitations of classical algorithms. These problems, prevalent in fields such as logistics, finance, and materials science often involve searching for the best solution from a vast number of possibilities. The efficiency of an optimisation algorithm is typically measured by the number of computational attempts required to find a solution within a specified level of accuracy. This research demonstrates that quantum annealing reduces the number of computational attempts needed to achieve a target approximation ratio by the same exponential level as the growth in attempts with system size for near-exact targets, a feat previously unattainable with classical methods. This signifies a substantial reduction in computational effort; for systems up to 125 sites, classical postprocessing alone can reach relaxed targets in order-unity attempts, indicating a significant speedup. The team quantified this performance using a new metric, STS(r), which measures attempts to approximate a solution, and found consistent outperformance of random baselines, enhancing concentration toward low-energy structures. The STS(r) metric, where ‘r’ denotes the approximation ratio, provides a standardised way to compare the performance of quantum and classical approaches, accounting for the trade-off